Single integration optimization of linear time-varying switched systems

Timothy M. Caldwell*, Todd D. Murphey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


This technical note considers the switching time optimization of time-varying linear switched systems subject to quadratic costalso potentially time-varying. The problem is formulated so that only a single set of differential equations need to be solved prior to optimization. Once these differential equations have been solved, the cost may be minimized over an arbitrary number of modes and mode sequences without requiring additional simulation. The differential equations that need to be simulated are as smooth as the system's vector fields, despite the fact that the optimization itself is nonsmooth. The technique is illustrated in examples from the literature.

Original languageEnglish (US)
Article number6069815
Pages (from-to)1592-1597
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - 2012


  • Algebraic linear quadratic switching time optimization (ALQSTO)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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